International Journal of Network Security & Its Applications (IJNSA), Vol.3, No.5, Sep 2011DOI : 10.5121/ijnsa.2011.3502 21 AMULTIPLE BALLOTS ELECTION SCHEME USING ANONYMOUS DISTRIBUTION Manabu Okamoto 1 1 Kanagawa Institute of Technology 1030 Shimo-Ogino, Atsugi, Kanagawa 243-0292, Japan [email protected]A BSTRACTElectronic voting is an important application for security protocols. Most existing voting schemes are designed for elections in which each voter has only one ballot. However, some elections permit voters to cast multiple ballots. In this paper, we present a new voting scheme in which each voter can have multiple ballots, and can vote for multiple candidates. The proposed scheme allows the voter to simply pick their candidates and post a single encrypted message. Anonymous distribution of secret information is used so that no one knows which information is being passed to whom. KEYWORDSElecronic voting, Anonymity 1.INTRODUCTIONElectronic voting is an important application for security protocols. Everybody hopes that electronic voting is as secure and efficient as traditional voting systems. It needs to ensure privacy, universal verifiability, fairness, and eligibility. Many electronic voting schemes have previously been proposed, though most of these voting schemes are intended for elections in which each voter has only one ballot. However, there are instances, in which each voter is permitted to cast multiple ballots [1], [2]. For example, a multiple ballot election is often used at a general meeting of stockholders. When applying the existing methods to a multiple ballot election, each voter would need to perform multiple actions. For example when I want to cast 3 ballots for Alice, I need to do 3 actions like sending 3 e-mails to the Vote-system server. These scheme are non-efficiency. In this paper, we present a new voting scheme in which each voter can have multiple ballots, and can vote for multiple candidates. The proposed scheme allows the voter to simply pick their candidates and post a single encrypted message. It is a very simple scheme and can reduce the cost of a voting system as well as the amount of effort required by the voter. The system can be divided into layers, so that voting in organizations is easily facilitated. An anonymous distribution scheme is used, employing secret information so that no one knows what’s actually being transmitted, or where it’s being sent. 2.RELATED WORKMany electronic voting schemes have pre viously been proposed. These are classified below. A. Shuffle
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8/3/2019 A Multiple Ballots Election Scheme Using Anonymous Distribution
International Journal of Network Security & Its Applications (IJNSA), Vol.3, No.5, Sep 2011
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The EAC then makes all data for the voting cards public on the BBS, without their encrypted
values. Figure 6 shows the prime numbers that correspond to each candidate. The EAC must be
truthful about this data because the hash values of cards have previously been made public.
We can easily compute from Figure 6 that:
Alice : 2 ballots (card: 8377 and 9067)
Bob : 3 ballots (card: 8707, 7127, and 3457)
Carol : 2 ballots (card: 4549 and 8971)
Therefore Bob has won, and the election is over.
We can check whether or not two ballots were cast on a single voting card, or if any other prime
number has been used.
7. SECURITY
A set of requirements on the electronic voting system must be satisfied by any secure voting
protocol [22]. These requirements can be grouped and summarized as follows:
・ Eligibility: Only eligible and authorized voters can vote.
・ Privacy: All votes must be kept secret. No one should be able to determine the value of the
vote cast by any given voter.
・ Fairness: Nothing must affect the voting. No participant is allowed to gain any knowledge
about the tally until the election deadline has passed.
・ Robustness: A coalition of voters or authorities cannot disrupt the results.
・ Universal Verifiability: A voting system is verifiable if anyone is able to verify that all votes
have been counted correctly. Any participant or observer can check that the final tally is
indeed the correct sum of all votes.・ Receipt-Freeness: No voter should be able to prove his vote to any other participant.
We will check that our scheme satisfies these requirements.
Eligibility: All voters need to be authenticated when sending ballots to Mix-net, therefore
double voting cannot occur as each voter can only connect to Mix-net once. Any ineligible
individual cannot participate in the vote, because he cannot receive any voting cards and cannot
connect to Mix-net. Only an eligible voter can receive a voting card from the EAC and send it to
Mix-net.
If the TF is corrupt, and attempts to change the voting cards so that their preferred candidate is
victorious, they will be thwarted. This is because the TF cannot change the prime numbers on a
voting card as they cannot associate them with any specific candidate. Every prime number thatcorresponds to each of the candidates is kept secret by the EAC. We therefore assume that the
EAC and the TF do not conspire together.
Privacy: Anonymity and privacy are achieved by using an anonymous distribution and Mix-net.
The safety of these can be increased by increasing the number of servers.
Fairness: If the TF cannot decrypt the prime product values which the voter has cast, then the
TF cannot decipher the tally. To achieve this, the encryption function consists of multiple
functions whose key is divided into multiple pieces, and distributed to multiple authorities. If
the TF cannot decrypt the votes, then only the number of voters can be known, not the number
of ballots. If we also need to keep the number of voters secret, then we have to divide the ballots
into multiple authorities.
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If the TF can decrypt and factor the values of the ballots, then the TF would know how many
ballots have been cast, but the TF still could not know which candidate is winning or losing.
This is because the TF cannot know how the prime numbers map to each candidate without
conspiring with the EAC.
Robustness: A dishonest voter cannot disrupt the voting. He cannot send more than one productof prime numbers because he cannot connect to Mix-Net more than once. If he disrupts his own
product of prime numbers, then he could only send the products of random primes. However, he
does not know which candidates, if any, correspond to those random primes. The TF can easily
ignore these. If by chance a random prime does correspond to a candidate, it is equivalent to
having correctly cast a vote for that candidate, but the voting itself cannot be disrupted.
Universal Verifiability: Universal verifiability is achieved through the use of the BBS. Anyone
is able to check the calculation for the total number of ballots, because the data is publicly
available on the BBS. Our scheme is very simple, and the calculations are trivial. One simply
has to get the data from the BBS and perform the count for each candidate, which is something
that can be done by anyone.
Receipt-Freeness: No voter can claim that a specific value on the BBS is the result of his ownvote, because he only knows the encrypted prime value and not the plain prime value. To satisfy
Receipt-Freeness, we recommend that the encryption function be probabilistic, because if the
public key of encryption function E is known, then we could easily encrypt the prime value on
the BBS, and check whether or not it is the same as the encrypted prime number on our voting
card.
One other security issue is now described. If the EAC were indeed corrupt, then he could
change the voting cards that have previously been created. For example, he could exchange the
prime value Ba in voting cards that correspond to Mr. A with value Bb that corresponds to Mr.
B. If a voter casts a ballot for Mr. A, and sends prime value Ba to Mix-net, then the corrupt EAC
could exchange these two values before making it public on the BBS. We will then tally the
vote for Mr. B, with the value Ba, which were originally intended for Mr. A.
To avoid this attack, we need to obtain the hash values of all the voting cards that correspond to
candidates before the start of the election. If the EAC wants to change any of the values used in
the voting cards, then this would easily be detected because anyone can calculate the hash value
of vote cards on a public BBS, and any voter can calculate the hash value of their own vote
cards. If the hash value is not same, then the EAC is suspect.
8. DISCUSSION
We will now discuss the efficiency of our proposed scheme. Products of prime values have been
used here; however, we could easily do the same thing by placing voting cards in order and then
encrypting and submitting that complete bundle, without needing any multiplications. Figure 7
shows such an encrypted bundle. We have to add dummy values into the submission, becauseotherwise it’s very easy to determine how many ballots have been cast by the length of the
bundle. This scheme is easier than ours as there are no multiplications to perform.
Figure 7. Encrypted bundle.
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Finally, we describe an important point in regards to our proposed method. We denote N as the
number of modulo bases in the crypto function. For example, in RSA, it is N = p×q for prime p
and q. In this scheme, we have to ensure that the maximum value of the product of prime
numbers is smaller than N . When there are a large number of voters, with many rights to vote,
and many candidates to vote for, we have to use a lot of prime values, and therefore have to uselarge primes whose product will also be very large. Thus, we need to make N a very large
number and need to ensure that sufficient computation time is allowed for. So our proposed
scheme is good for small election which consists of many small sub-groups.
9. CONCLUSION
We have proposed a new multiple ballot election scheme using an anonymous distribution. In
this scheme each voter would need NOT to perform multiple actions. Each voter requires only
one action to cast multiple ballots. It would contribute to reducing the burden on voters. Voters
can cast ballots by only one e-mail or Web-access. It is a very simple scheme that supports
eligibility, privacy, fairness, robustness, universal verifiability, and receipt-free operation. We
do not need the big calculation. All a voter has to do is to multiply values in voting cards he got.Our proposed scheme is also very effective when organization is divided into layers. We can
divide a vote act into some groups. It would contribute to reducing the burden on voting-system.
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